Abstract

The ribosome is an extremely important molecular organelle for the cellular workings. It is of interest to a wide array of scientists with spanning interests from the fundamental questions of life and individuality to the practical fields of medicine development and pharmacology. Here we present network analysis on interactions between the ribosomal constituents – ribosomal RNA (rRNA) and ribosomal proteins (rProteins) in the context of the accretion model for ribosomal evolution [1]. We demonstrate that different evolutionary phases give deferring network statistics from one another, furthermore the ribosomal networks’characteristics are a result of their degree distributions when considering the ribosome as whole evolving entity. We also show that community detection algorithms can be used to define rRNA and rProtein folding domains, and show the interdependence between rRNA and rProtein interactions.

Image('./figs/Figure_1_A+B_rRNA+rProtein_Evolution-01.jpg')

Image('./figs/RING_energy_dist.png')

plot_nodes(EsCo_nodes)

louvain5, lv5_df = plot_louvain(5, G_EsCo, make_plot=True)

Resolution: 5
Number of partitions: 74
Modularity: 0.7958522770514428

prtn_mod_res_df, nodes_prtn_df = make_prtn_mod_res_df(resolution, G_EsCo)

# Create traces
trace0 = go.Scatter(
    x = prtn_mod_res_df['Resolution'],
    y = prtn_mod_res_df['Num_Partitions'],
    mode = 'lines',
    name = 'Partitions'
)
trace1 = go.Scatter(
    x = prtn_mod_res_df['Resolution'],
    y = prtn_mod_res_df['Modularity'],
    mode = 'lines',
    name = 'Modularity',
    yaxis='y2'
)


layout = go.Layout(
    title='Modularity and Parition Number vs. Louvain Resoution',
    xaxis=dict(
        title='Louvain Resolution'
    ),
    yaxis=dict(
        title='Number of Partitions'
    ),
    yaxis2=dict(
        title='Modularity',
        titlefont=dict(
            color='rgb(148, 103, 189)'
        ),
        tickfont=dict(
            color='rgb(148, 103, 189)'
        ),
        overlaying='y',
        side='right'
    )
)

data = [trace0, trace1]
fig = go.Figure(data=data, layout=layout)
iplot(fig)

nodes_prtn_df

	node	louvain1.0	louvain1.5	louvain2.0	louvain2.5	louvain3.0	louvain3.5	louvain4.0	louvain4.5	louvain5.0	louvain5.5	louvain6.0	louvain6.5	louvain7.0	louvain7.5	louvain8.0	louvain8.5	louvain9.0	louvain9.5	louvain10.0	louvain10.5	louvain11.0	louvain11.5	louvain12.0	louvain12.5	louvain13.0	louvain13.5	louvain14.0	louvain14.5	louvain15.0	louvain15.5	louvain16.0	louvain16.5	louvain17.0	louvain17.5	louvain18.0	louvain18.5	louvain19.0	louvain19.5	louvain20.0
0	n0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
1	n1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2	n10	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
3	n100	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5
4	n1000	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
10556	n9995	17	4	14	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4
10557	n9996	17	4	14	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4
10558	n9997	17	4	14	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4
10559	n9998	17	4	14	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4
10560	n9999	17	4	14	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4

10561 rows × 40 columns

plot_nodes_partitions(lv10_df[lv10_df.Object == 'uL02'])

plot_nodes(SaCe_rPro_nodes)

# Create traces
trace0 = go.Scatter(
    x = prtn_mod_res_df['Resolution'],
    y = prtn_mod_res_df['Num_Partitions'],
    mode = 'lines',
    name = 'Partitions'
)
trace1 = go.Scatter(
    x = prtn_mod_res_df['Resolution'],
    y = prtn_mod_res_df['Modularity'],
    mode = 'lines',
    name = 'Modularity',
    yaxis='y2'
)


layout = go.Layout(
    title='Modularity and Parition Number vs. Louvain Resoution',
    xaxis=dict(
        title='Louvain Resolution'
    ),
    yaxis=dict(
        title='Number of Partitions'
    ),
    yaxis2=dict(
        title='Modularity',
        titlefont=dict(
            color='rgb(148, 103, 189)'
        ),
        tickfont=dict(
            color='rgb(148, 103, 189)'
        ),
        overlaying='y',
        side='right'
    )
)

data = [trace0, trace1]
fig = go.Figure(data=data, layout=layout)
iplot(fig)

louvain4, df = plot_louvain(4, G_SaCe_rPro)

Resolution: 4
Number of partitions: 151
Modularity: 0.8093295900148612

plot_nodes_partitions(df[df.rProtein == 'uL02'], lines=True)

walktrap2 = walktrap_output(2)
walktrap4 = walktrap_output(4)
walktrap6 = walktrap_output(6)
walktrap8 = walktrap_output(8)
walktrap10 = walktrap_output(10)
walktrap100 = walktrap_output(100)

Walktrap steps: 2
Optimal count: 7293
Modularity: 0.10447832211050502
 
Walktrap steps: 4
Optimal count: 7293
Modularity: 0.10447832211050502
 
Walktrap steps: 6
Optimal count: 7293
Modularity: 0.10447832211050502
 
Walktrap steps: 8
Optimal count: 7293
Modularity: 0.10447832211050502
 
Walktrap steps: 10
Optimal count: 7293
Modularity: 0.10447832211050502
 
Walktrap steps: 100
Optimal count: 7293
Modularity: 0.10447832211050502
 

p1 = Image('./shortest_path/adjlist_ph1.txt.png', width=400)
p2 = Image('./shortest_path/adjlist_ph2.txt.png', width=400)
p3 = Image('./shortest_path/adjlist_ph3.txt.png', width=400)
p4 = Image('./shortest_path/adjlist_ph4.txt.png', width=400)
p5 = Image('./shortest_path/adjlist_ph5.txt.png', width=400)
p6 = Image('./shortest_path/adjlist_ph6.txt.png', width=400)
display(p1,p2,p3,p4,p5,p6)

p1 = Image('./shortest_path/conc_adjlist_ph1.txt.png', width=400)
p2 = Image('./shortest_path/conc_adjlist_ph2.txt.png', width=400)
p3 = Image('./shortest_path/conc_adjlist_ph3.txt.png', width=400)
p4 = Image('./shortest_path/conc_adjlist_ph4.txt.png', width=400)
p5 = Image('./shortest_path/conc_adjlist_ph5.txt.png', width=400)
p6 = Image('./shortest_path/conc_adjlist_ph6.txt.png', width=400)
display(p1,p2,p3,p4,p5,p6)